cf {controlfunctionIV} | R Documentation |
Control-Function
Description
Implement the control function method for the inference of nonlinear treatment effects.
Usage
cf(formula, d1 = NULL, d2 = NULL)
Arguments
formula |
A formula describing the model to be fitted. |
d1 |
The baseline treatment value. |
d2 |
The target treatment value. |
Details
For example, the formula Y ~ D + I(D^2)+X|Z+I(Z^2)+X
describes the models
Y = \alpha_0 + D\beta_1 + D^2\beta_2 + X\phi + u
and
D = \gamma_0 + Z\gamma_1 + Z^2\gamma_2 + X\psi + v
.
Here, the outcome is Y
, the endogenous variables is D
, the baseline covariates are X
, and the instrument variables are Z
. The formula environment follows
that in the ivreg function in the AER package. The endogenous variable D
must be in the first term of the formula for the outcome model.
If either one of d1
or d2
is missing or NULL
, CausalEffect
is calculated assuming that the baseline value d1
is the median of the treatment and the target value d2
is d1+1
.
Value
cf
returns an object of class "cf", which is a list containing the following components:
coefficients |
The estimate of the coefficients in the outcome model. |
vcov |
The estimated covariance matrix of coefficients. |
CausalEffect |
The causal effect when the treatment changes from |
CausalEffect.sd |
The standard error of the causal effect estimator. |
CausalEffect.ci |
The 95% confidence interval of the causal effect. |
References
Guo, Z. and D. S. Small (2016), Control function instrumental variable estimation of nonlinear causal effect models, The Journal of Machine Learning Research 17(1), 3448–3482.
Examples
data("nonlineardata")
Y <- log(nonlineardata[,"insulin"])
D <- nonlineardata[,"bmi"]
Z <- as.matrix(nonlineardata[,c("Z.1","Z.2","Z.3","Z.4")])
X <- as.matrix(nonlineardata[,c("age","sex")])
cf.model <- cf(Y~D+I(D^2)+X|Z+I(Z^2)+X)
summary(cf.model)